import numpy as np
import matplotlib.pyplot as plt
import math

def normal_distribution(x,mu,sigma):
    return np.exp( -1* ((x-mu) ** 2) / ( 2 * (sigma ** 2)) ) / (math.sqrt( 2 * np.pi) * sigma)
mu1, sigma1 = 10, 2 ** 0.5
mu2, sigma2 = 12, 3 ** 0.5
x1 = np.linspace(mu1 - sigma1 * 6, mu1 + sigma1 * 6, 100)
x2 = np.linspace(mu2 - sigma2 * 6, mu2 + sigma2 * 6, 100)
y1 = normal_distribution(x1, mu1, sigma1)
y2 = normal_distribution(x2, mu2, sigma2)
plt.plot(x1, y1, 'r')
plt.plot(x2, y2, 'b')
plt.legend()
plt.grid()
plt.show()